Recently, there is a tremendous interest in single-carrier (SC) block transmission with cyclic prefix (CP) or unique word (UW) being appended before each data block. Compared to multi-carrier modulation, the SC modulation has lower peak-to-average power ratio and lower sensitivity to carrier frequency offset. Moreover, with CP or UW, such an SC block transmission allows the design of frequency-domain equalizers (FDEs) that can significantly reduce the complexity in suppressing the inter-symbol interference (ISI) caused by the frequency selectivity of the channel. (see D. Falconer, S. L. Ariyavisitakul, A. Benyamin-Seeyar, and B. Eidson, ‘Frequency domain equalization for single-carrier broadband wireless systems’, IEEE Communications Magazine, vol. 40, no. 4, pp. 27-36, April 2002.)
When applied to cellular communications, an SC modulation system has additional performance-limiting factor of co-channel interference (CCI). To overcome these channel impairments, various joint CCI and ISI suppression schemes have been developed. In A. Ginesi, G. M. Vitetta, and D. D. Falconer, ‘Block channel equalization in the presence of a cochannel interferent signal’, IEEE Journal on Selected Areas in Communications, vol. 17, no. 11, pp. 1853-1862, November 1999, linear and decision feedback time-domain equalizers (TDEs) are derived in typical cellular systems, where one dominant interferer contributes mainly to the data-like CCI. However, these TDEs in general suffer from high computational complexity, especially in inverting the signal correlation matrix and multiplying the equalization matrix to the observation vector.
To reduce the computational complexity, an FDE may be designed as is the common practice for ISI suppression. However, a direct conversion of the linear minimum mean-squared error (LMMSE) TDE to an FDE does not lead to a significant complexity reduction. This is because the frequency-domain correlation matrix of the CCI plus Gaussian noise component is no longer a diagonal matrix. Thus, the LMMSE FDE still requires the inversion of an un-structured matrix and the matrix-vector multiplication rather than simple one-tap equalization.
To overcome these shortcomings, the correlation matrix may be replaced with an equivalent matrix whose structure can be exploited in the complexity reduction. Such replacement techniques have been frequently used in signal processing and the approximations are justified by the theory of asymptotically equivalent sequences of matrices (see R. M. Gray, ‘Toeplitz and circulant matrices: a review’, Information theory laboratory, Stanford univ., Stanford, Calif.). Among various asymptotic equivalences, the equivalence between the sequence of Toeplitz matrices and that of circulant matrices has been of the foremost interest. However, when the receive filter output is over-sampled to better capture the channel response and the second-order statistics of the data-like CCI, the CCI plus noise correlation matrix is not Toeplitz.
The present invention provides a method and apparatus for frequency domain equalization to jointly suppress ISI and CCI that has much lower computational complexity than the LMMSE equalizers while resulting in almost no performance degradation compared to the LMMSE equalizers. Motivated by the facts that the data-like CCI is, or is well approximated as, a wide-sense cyclostationary (WSCS) random process and that the double Fourier transform of its autocorrelation function consists of impulse fences with equal spacing, a block matrix approximation with diagonal blocks to the frequency-domain correlation matrix is invoked. Since the inversion of such a block matrix can be performed efficiently and the inverse is also a block matrix with diagonal block, the resultant FDE for joint ISI and CCI suppression obtained from the LMMSE FDE through the replacement has much lower computational complexity than the LMMSE equalizers.